Diffusion theory applied to radiant energy distribution and albedo of snow

The penetration of radiation into snow is assumed to follow Fick's second law of diffusion with a term for simultaneous absorption. From this, the distribution of radiant energy in a deep homogeneous snow cover, a laminated snow cover, and a snow cover with an absorbing surface beneath is deduced. An equation for albedo is also derived. The penetration phenomenon is then analyzed in terms of the physical processes occurring and formulated as a random walk process. After a correction is made for a certain amount of nondiffuse radiation in the snow, more accurate equations for energy distribution and albedo are obtained. These results are applied to the theory of radiation measurement in snow. After experimental procedures were established on the Blue Glacier summer firn, field data were collected from winter snow at Alta, Utah, and used to check the theoretical equations for albedo and transmission to a black surface. The agreement of theory and experiment is very satisfactory.